Beethoven and Shakespeare conceived their late works either side of 50. These days, however, the likes of Leonard Cohen, Neil Diamond and PD James are producing what can only be described as 'very late works'

IN THE year before he died, Beethoven somehow constructed in the silence of his mind a fiendishly difficult string quartet, the Grosse Fuge. (He was by then unable to hear anything he composed.) Shakespeare, in the last of the plays that academic posterity will unambiguously attribute to him, brought together themes of paternal loss and creative decline in The Tempest. Philip Larkin, fearing that poetry had given him up after the publication of what would prove to be his final collection, focused his concentration to deliver just one more major poem, Aubade, distilling his terror of death.

These are all pieces the critics would categorise as late work: words or music in which an artist combines a lifetime of experience with the technique perfected through a long career to offer a climactic contribution to the art form they have served. But check the dates and you'll find that Beethoven, Shakespeare and Larkin were just either side of 50 when they committed their last thoughts. Increasingly, by contemporary standards, the Grosse Fuge, The Tempestand Aubadewould stand as transitional works of middle age.

This autumn, PD James published her latest crime novel, The Private Patient, at the age of 88. And she is not the oldest author in the autumn lists: former Booker prize winner Stanley Middleton, 89 in August, has recently published Her Three Wise Men. But James and Middleton are more or less adolescents in comparison with Elliott Carter, who this summer became the first living composer to be granted a centenary concert at the BBC Proms. Carter is still composing at an age when most people are doing the opposite: this year's celebrations included a new flute concerto, and two more pieces are said to be in preparation.

In pop and rock, long regarded as a business for the young and one in which there has been a sentimental respect for early death, the best reviews of the year for live performance have been shared by Leonard Cohen (73) and Neil Diamond (67). The nervous showbusiness tradition of performers pretending to be younger than they are - fearful of seeming like the parents of their fans - may soon be reversed, with rookie musicians shifting their birth dates backwards, like army volunteers.

IT CAN SEEM ungallant to make a song and dance about the age at which people are still singing and dancing. It's wise to be wary of Queen Mother syndrome, the process by which, in a famous figure's final years, almost any evidence of undamaged faculties is met with cries of: "Aren't they amazing? At their age!" But there has been a marked change in the traditional trajectory of an artistic career. The general increase in longevity bestowed by medical developments has combined with a growing respect for professional veterans, to create a new genre: very late work.

What makes these pieces intriguing is the expectation of an even more concentrated expression of the values traditionally attributed to late work: a deeper accumulation of history, wisdom, expertise. It's the same impulse that leads local museums to interview senior members of their communities for oral history projects. The Tempestis a good example of this kind of end-of-career piece. The play demonstrates Shakespeare's poetic maturity and hard-learned stagecraft and, in the moment when the magician Prospero breaks and jettisons the tools of his trade, encourages us to take this as the closest we will ever get to a memoir from an irritatingly invisible author.

These conventional expectations of late work - the serenity of seniority, the perfection of a philosophy - have been challenged by the literary critic Edward Said in his influential book On Late Style(2002). Said, a dedicated contrarian, argued that what made autumnal culture most interesting was not that the writer had come to some kind of final understanding of their world and their work, but that they had failed to do so. Career codas such as Beethoven's Grosse Fugeor Missa Solemnis- dark, dense, dragged out of deafness - were a statement, he argued, of "intransigence, difficulty and unresolved contradiction".

As Said freely acknowledged, his interest in this subject came partly from the knowledge that his own book would rank among his late work: he had begun the lecture programme that inspired it following the diagnosis of leukaemia, which killed him in 2003, at the age of 67. On Late Styleis itself an example of the kind of final writing that the volume approvingly cites. Said's theories about creativity in its fading days are difficult, intransigent and sometimes contradictory.

But his views are illuminating when it comes to very late work - in particular, PD James's work of her 88th year. Baroness James of Holland Park has worked in a conservative literary tradition - the classic English detective mystery - and, in that sense, is the kind of artist to whom Said would least have warmed. In some ways, The Private Patient, her 19th novel, does fit the sentimental template of stories that sit towards the end of a writer's bookshelf: there are several reflections on the unstoppable passage of time, the finality of death and the consolation of relationships. However, even so late in the day, James - like Said's Beethoven - also struggles against the subjects and structures with which she works.

For example, for the first time in her books, she explicitly and graphically describes the moment of death from the perspective of the murder victim. This passage suggests an attempt to make the fullest possible engagement with the ultimate crime that has been her great theme. There is also little that is serene and accepting in the atmosphere of this book. Christian religious faith, a recurrent touchstone for James's characters, seems in The Private Patientno more than a comforting ritual: a suicide takes place on holy ground, and James's sentiments throughout feel closer to the atheistic philosophy of Philip Larkin - "what will survive of us is love" - than any sense that the many corpses in her story are happy in paradise. Nor is there any comforting dispensation of justice, of the sort that Commander Adam Dalgliesh easily achieved in his early cases. Key issues remain, to borrow a favourite Said word, unresolved.

Stanley Middleton is another author who works in a traditional form - "well-made" novels about the provincial middle classes - and his very late novels find him worrying away at the literary and social values that have informed his work. There is also the feeling of absolutely authentic reportage of the experience of being old in a culture biased towards youth: the experiences of illness, bereavement, pensions and insurance bureaucracy. When, in a recent novel, Middleton featured a character with Alzheimer's, there was a moving sense of a report being sent back from a massacre by one of the few to escape.

OF COURSE, THERE can be weaknesses in the novels of advanced seniority. The younger characters in both James and Middleton speak an English improbably free of swearing and text abbreviations; and the prevalence in James's books of unmarried brothers and sisters who share houses perhaps marks her as an Edwardian, born in a period when such living arrangements were rather more common. But, at their best, these books offer the pleasure of writers completely at ease with their craft, and still urgently concerned with life and society.

What's especially impressive about James is her continuing energy. Whereas Graham Greene's later works were eccentric novellas - a classic example of the tendency of climactic creativity towards fragments - The Private Patientalternates numerous viewpoints over 400 pages. Commending James for such productivity, however, again raises one of the risks of very late work: the tendency to praise the existence of the work rather than its content. At the centenary concerts for Elliott Carter, there was a feeling that concert-goers who would instinctively dislike his complex and edgy compositions were simply applauding his longevity. And yet Carter represents the fascinating contradiction of a modernist centenarian - an old artist still interested in newness.

IN THE SAME way, anyone who went to see Leonard Cohen or Neil Diamond this year in some mood of patronising surprise at their ability to keep going would soon have realised that the prevailing spirit of these performances was not heritage conservation but reinvention and experimentation. Although both performed many old numbers, the point was what they brought to them now, after periods of personal difficulties in both cases.

The usual objection to singers in the final phase of their careers has been that their voices go. During the final tours of Frank Sinatra and Nina Simone, audiences had to fight an instinct to shout out for an ear, nose or throat surgeon in the house. But what's fascinating about Cohen in particular is that, if his voice has gone, it has simply gone to another place - and, probably, a better one. Listening to Cohen's 1970s and 1980s recordings after seeing him perform in Dublin and London this year, I was surprised to find that what had once seemed definitive recordings of Hallelujahand Suzannefelt somehow light and trivial. Now that he has taken the sensible precautions of giving up smoking and taking up yoga, there is a remarkable combination of gravity and clarity in Cohen's tones.

Admittedly, it's hard to imagine the singers continuing for as long as the novelists and the composers - Diamond or Cohen with guitars slung round their necks at the age of 88 or 89 - but a society in which the ageing often feel marginalised or ignored seems to be redressing the balance in culture. Roll over, Beethoven: this is what we mean by late work. ( Guardian service)

• The Private Patientby PD James and Her Three Wise Menby Stanley Middleton are both published in hardback